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A process that fills packages is stopped whenever a
Chapter 4, Problem 8E(choose chapter or problem)
A process that fills packages is stopped whenever a package is detected whose weight falls outside the specification. Assume that each package has probability 0.01 of falling outside the specification and that the weights of the packages are independent.
a. Find the mean number of packages that will be filled before the process is stopped.
b. Find the variance of the number of packages that will be filled before the process is stopped.
c. Assume that the process will not be stopped until four packages whose weight falls outside the specification are detected. Find the mean and variance of the number of packages that will be filled before the process is stopped.
Questions & Answers
QUESTION:
A process that fills packages is stopped whenever a package is detected whose weight falls outside the specification. Assume that each package has probability 0.01 of falling outside the specification and that the weights of the packages are independent.
a. Find the mean number of packages that will be filled before the process is stopped.
b. Find the variance of the number of packages that will be filled before the process is stopped.
c. Assume that the process will not be stopped until four packages whose weight falls outside the specification are detected. Find the mean and variance of the number of packages that will be filled before the process is stopped.
ANSWER:Answer:
Step 1 of 4:
Given, a process is their to fill packages, that process is stopped whenever a package is detected whose weight falls outside the specification.
We have to assume that each package has probability 0.01 of falling outside the specification and the weights of the packages are independent.
X = the number of packages that will be filled before the process is stopped.
Let X follows Geometric distribution and probability mass function of the Geometric distribution is
P(x) = p (1 - p , x = 1, 2, …..
Where, p = 0.01